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A remark on infinitary languages

Published online by Cambridge University Press:  12 March 2014

Jörg Flum
Jörg Flum*
Affiliation:
Albert-Ludwigs-Universität, Freiburg i. BR., W. Germany
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Extract

In his paper [1] Chang provides among other things answers to questions of the following type: Given two models and of powers α and β, respectively, what is the least λ such that implies His proofs are by induction on the quantifier rank of formulas and they use an idea which in the case of ordinary first-order language goes back to Ehrenfeucht and Fraïssé. But, as we show, one can easily prove that if λ is big compared with κ and with the cardinality of the universe of the structure , then every L∞κ-formula is equivalent modulo the set of all Lλκ-sentences which hold in to a Lλκ-formula. From this, Chang's results follow immediately. The same method can be applied to similar problems concerning generalized languages.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 3 , September 1971 , pp. 461 - 462
Copyright
Copyright © Association for Symbolic Logic 1972

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References

[1]Chang, C. C., Some remarks on the model theory of infinitary languages, The syntax and semantics of infinity languages, edited by Barwise, Jon, Springer-Verlag, Berlin, 1968, pp. 36–63.CrossRefGoogle Scholar